Mixed-state quantum anomaly and multipartite entanglement

Understand

Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter.

• Here we explore a surprising connection between mixed state entanglement and 't Hooft anomaly.
• More specifically, we consider lattice systems in $d$ space dimensions with anomalous symmetry $G$ where the anomaly is characterized by an invariant in the group cohomology $H^{d+2}(G,U(1))$.
• We show that any mixed state $\rho$ that is strongly symmetric under $G$, in the sense that $G\rho\propto\rho$, is necessarily $(d+2)$-nonseparable, i.e.